Optimization of Sliding Mode Controller to control Three-Tank System Based on Lagrange Multipliers Optimization Algorithm

This manuscript designs a sliding mode controller to adjust height of nonlinear three-tank system of two inputs and one output. This controller is a first order sliding mode controller in which several multipliers have been added to optimize the controller performance. To optimize these multipliers, a Lagrange multipliers optimization based is used for the first time. In comparison with evolutionary algorithms, it will be shown that using the Lagrangian optimization algorithm needless any iterations which makes this algorithm very fast and thus suitable for applications such as real-time systems. Finally, simulation results show that the proposed optimal method offers a faster response against uncertainties when the height of tank is also optimized.